Content uploaded by Onur Dizdar
Author content
All content in this area was uploaded by Onur Dizdar on Sep 21, 2022
Content may be subject to copyright.
A Rate-Splitting Strategy to Enable Joint Radar
Sensing and Communication with Partial CSIT
Rafael Cerna-Loli, Onur Dizdar and Bruno Clerckx
Department of Electrical and Electronic Engineering
Imperial College London, London, U.K.
Email: {rafael.cerna-loli19, o.dizdar, b.clerckx}@imperial.ac.uk
Abstract—In order to manage the increasing interference
between radar and communication systems, joint radar and
communication (RadCom) systems have attracted increased at-
tention in recent years, with the studies so far considering
the assumption of perfect Channel State Information at the
Transmitter (CSIT). However, such an assumption is unrealistic
and neglects the inevitable CSIT errors that need to be considered
to fully exploit the multi-antenna processing and interference
management capabilities of a joint RadCom system. In this work,
a joint RadCom system is designed which marries the capabilities
of a Multiple-Input Multiple-Output (MIMO) radar with Rate-
Splitting Multiple Access (RSMA), a powerful downlink commu-
nications scheme based on linearly precoded Rate-Splitting (RS)
to partially decode multi-user interference (MUI) and partially
treat it as noise. In this way, the RadCom precoders are optimized
in the presence of partial CSIT to simultaneously maximize the
Average Weighted Sum-Rate (AWSR) under QoS rate constraints
and minimize the RadCom Beampattern Squared Error (BSE)
against an ideal MIMO radar beampattern. Simulation results
demonstrate that RSMA provides the RadCom with more robust-
ness, flexibility and user rate fairness compared to the baseline
joint RadCom system based on Space Division Multiple Access
(SDMA).
Index Terms—Radar-communication (RadCom), MIMO radar,
rate-splitting multiple access (RSMA), Alternating Direction
Method of Multipliers (ADMM), partial channel state informa-
tion (CSI) at the transmitter (CSIT).
I. INTRODUCTION
Radar systems are vital in public safety and military appli-
cations, where it is necessary to identify relevant targets with
a high resolution estimation of their associated angle, range
and velocity. This requires that radar systems are allocated
sufficient electromagnetic (EM) spectrum resources to collect
all the necessary information with a single radar pulse [1].
On the other hand, next generation wireless communication
systems, such as the 5G-New Radio (NR) mobile commu-
nication networks and Internet of Things (IoT), also demand
large spectrum resources to offer high data rate services with a
guaranteed Quality-of-Service (QoS) level. Due to insufficient
available bandwidth, specially in sub-10 GHz bands, increased
spectrum congestion and inter-system interference is expected
without careful simultaneous deployment planning of radar
and communication systems [2]. This spectrum congestion
issue is the focus of Communication and Radar Spectrum
Sharing (CRSS) research [3], where different studies have
recently been made in order to optimize different perfor-
mance metrics of spectrum sharing radar and communication
(RadCom) systems by employing techniques such as interfer-
ence mitigation, beamforming, and optimum waveform design.
Nevertheless, these efforts can generally be classified into two
categories: coexistent RadComs and joint RadComs.
Coexistent RadCom design considers that the radar and
communication parts are deployed separately, with indepen-
dent hardware and signal processing units, but share substan-
tial information between each other in order to optimize their
individual performance [4]. To achieve this, the RadCom may
employ a control center or mediator to relay the necessary
information and keep them synchronized. Although theoreti-
cally functional, including this external element would greatly
increase hardware costs and required computational power.
This issue is bypassed with a joint RadCom design as radar and
communication modules are deployed with unified hardware
and signal processing units [5]. Thus, this approach is also the
most suitable for a long-term development of wireless systems
and EM spectrum allocation. Advantages of a joint design
also include highly-directional beamforming, minimum delay,
enhanced security and privacy, and dynamic computational
resource allocation.
This paper follows our earlier work in [6] and extends
it to optimize the precoders of a joint RadCom system in
the more realistic and important partial CSIT setting for the
first time. In order to achieve this, a Rate-Splitting Multiple
Access (RSMA) communications module is considered to
operate jointly with a Multiple-Input Multiple-Output (MIMO)
radar module. As it will be demonstrated in the following
sections, RSMA constitutes a robust interference manage-
ment framework in the presence of CSIT errors that aims
to mitigate multi-user interference (MUI) by splitting the
user data streams into common streams decoded by all users
(partially decoding MUI), and private streams decoded only
by its intended user (partially treating MUI as noise) [7].
In the context of a joint RadCom design with partial CSIT,
RSMA offers a special advantage as the beampattern of
the common stream can be used to approximate a highly-
directional transmit beampattern, which greatly increases the
detection capabilities of the MIMO radar module, while also
providing flexibility to comply with QoS rate constraints.
II. JOINT RA DCO M SYS TE M MOD EL
Consider a joint RadCom, with a uniform linear array of
Nttransmit antennas and a total available transmit power Pt,
arXiv:2105.00633v1 [eess.SP] 3 May 2021
that serves Ksingle antenna communication users, indexed
by the set K={1, . . . , K}, and tracks a single radar target
as depicted in Fig. 1. It employs an RSMA communications
module and a mono-static MIMO radar module that share
information, such as transmit communication signals and radar
target parameters, to perform joint precoder optimization.
A. RSMA-RadCom Signal Model
In this subsection, the operation of the RSMA communica-
tions module is described. The intended message for user-k
Wkis split into a common part Wc,k and a private part Wp,k.
Then, the common parts of all Kusers {Wc,1, . . . , Wc,K }
are encoded into a single common stream sc, while the
private parts {Wp,1, . . . , Wp,K}are encoded into Kdifferent
private streams {s1, . . . , sK}. The data stream vector s=
[sc, s1, . . . , sK]T∈C(K+1)×1is linearly precoded using the
precoder P= [pc,p1,...,pK]∈CNt×(K+1), where pcis
the common stream precoder and pkis the private stream
precoder for user-k. The transmitted signal x∈CNt×1is then
given by
x=Ps =pcsc+
K
X
k=1
pksk.(1)
It is proposed that the communication signal in (1) is also
used for MIMO radar purposes following the work in [8]. It
is shown in [8] that the optimum design of the transmit signal
covariance matrix Rxof a MIMO radar can be achieved in a
simplified manner by generating the transmitted signal xas a
linear combination of independent signals, which effectively
matches the signal model in (1). In this way, optimization of
Rxis reduced to optimization of the precoder matrix P.
The signal received by user-kis then given by
yk=hH
kPs +nk
=hH
kpcsc+hH
kpksk+
MUI
z }| {
X
j6=k,j∈K
hH
kpjsj+nk,
(2)
where hk∈CNt×1is the channel between the RadCom and
user-k, and nk∼ CN (0, σ 2
n,k)is the Additive White Gaussian
Noise (AWGN) at user-k. Without loss of generality, it is
assumed that σ2
n,k =σ2
n= 1,∀k∈ K.
The Signal-to-Interference-and-Noise Ratio (SINR) of the
common stream at user-kis given by
γc,k =|hH
kpc|2
Pk∈K |hH
kpk|2+σ2
n,k
.(3)
After decoding the common stream, Successive Interference
Cancellation (SIC) is applied to remove the obtained estima-
tion from the received signal ykand then decode the private
stream. The SINR of the private stream at user-kis then given
by
γk=|hH
kpk|2
Pj6=k,j∈K |hH
kpj|2+σ2
n,k
.(4)
Therefore, the achievable rate of the common stream for user-
kis Rc,k(P) = log2(1 + γc,k)and the achievable rate of
Fig. 1. Proposed joint RadCom system model.
its corresponding private stream is Rk(P) = log2(1 + γk).
In order to ensure that all Kusers are able to decode the
common stream, it must be transmitted at a rate no larger
than Rc(P) = min{Rc,1(P), . . . , Rc,K (P)}, with the portion
of the total common stream rate assigned to user-kbeing given
by Ck, such that Pk∈K Ck=Rc(P).
B. Channel State Information Model
The Channel State Information (CSI) is modeled by H=
ˆ
H+˜
H, where H= [h1,...,hK]is the real channel,
ˆ
H= [ˆ
h1,...,ˆ
hK]is the estimated channel at the RadCom,
and ˜
H= [˜
h1,...,˜
hK]is the estimation error matrix. It is also
assumed that hk,ˆ
hkand ˜
hkhave i.i.d complex Gaussian en-
tries drawn from the distributions CN (0, σ2
k),CN (0, σ 2
k−σ2
e,k)
and CN (0, σ 2
e,k)respectively, for each k∈ K. The parameter
σ2
e,k ,σ2
kP−α
tis the CSIT error power for user-k, where
α∈[0,∞)is the CSIT quality scaling factor [9]. α→ ∞
corresponds to perfect CSIT while α= 0 represents partial
CSIT with finite precision. In this work, perfect Channel
State Information at the Receiver (CSIR) and partial CSIT
are assumed, where the latter indicates that the RadCom
only knows ˆ
Hand the conditional CSIT error distribution
fH|ˆ
H(H|ˆ
H).
III. PERFORMANCE METRICS AND PROB LE M
FOR MU LATI ON
In this section, the performance metrics for communications
and radar sensing are introduced and used to define the joint
RadCom optimization problem.
A. Communications Metric: Average Weighted Sum-Rate
To achieve maximum user rates, (3) and (4) need to be
jointly maximized. However, computation of the exact pre-
coders that maximize the common and private SINRs is not
possible with partial CSIT. On one hand, a naive strategy
would be to treat the estimated channel ˆ
Has perfect CSIT,
which would result in increased MUI, inefficiency in the
precoder power allocation and, ultimately, transmission at
undecodable rates. On the other hand, a more resilient strategy
is to adapt the precoder matrix ˆ
P=P(Pt,ˆ
H)to send
the common stream and the private streams at their Ergodic
Rates (ERs), representations of the long-term rates over all
channel states for the distribution fH(H). The ERs for user-
kare given by EH{Rc,k}and EH{Rk}for the common and
private stream respectively. Additionally, the common ER to
guarantee successful decoding by all Kusers is given by
mink{EH{Rc,k}}K
k=1.
Although the ERs cannot be directly maximized without
perfect CSIT, optimization of the ERs under partial CSIT can
be achieved by maximizing the average Rates (ARs), short-
term measures of the expected performance over fH|ˆ
H(H|ˆ
H),
of the common and private streams for each channel esti-
mate ˆ
H. The ARs for user-kare then given by ¯
Rc,k ,
EH|ˆ
H{Rc,k|ˆ
H}and ¯
Rk,EH|ˆ
H{Rk|ˆ
H}for the common and
private stream respectively. Additionally, the common AR for
all users is given by ¯
Rc,mink{EH|ˆ
H{Rc,k|ˆ
H}}K
k=1. The
Average Weighted Sum-Rate (AWSR) metric is then defined
as
AWSR(ˆ
P) = X
k∈K
µk(¯
Ck+¯
Rk(ˆ
P)),(5)
where µkis the weight assigned to user-k.
B. Radar Sensing Metric: Beampattern Squared Error
As shown in [8], the detection capabilities of a MIMO radar
can be improved by appropriately designing the covariance
matrix Rx∈CNt×Ntof the transmitted signal xto approxi-
mate a highly directional transmit beampattern Pd. Thus, the
radar sensing metric, the Beampattern Squared Error (BSE),
can be defined as PM
m=1 |αPd(θm)−aH
t(θm)Rxat(θm)|2,
where αis the scaling factor of Pd,Mis the total number
of azimuth angle grids, θmis the mth azimuth angle grid,
at(θm) = [1, ej2πδ sin(θm, . . . , ej2π(Nt−1)δsin(θm)]T∈CNt×1
is the transmit antenna array steering vector at direction θm
and δis the normalized distance in units of wavelengths
between antennas. In the context of the proposed RadCom
transmission, the BSE is then given by
BSE(ˆ
P) =
M
X
m=1
|αPd(θm)−aH
t(θm)ˆ
Pˆ
PHat(θm)|2,(6)
where Pt(θm) = aH
t(θm)ˆ
Pˆ
PHat(θm) =
aH
t(θm)ˆ
pcˆ
pH
cat(θm) + PK
k=1 aH
t(θm)ˆ
pkˆ
pH
kat(θm)is
the RadCom transmit beampattern gain at direction θm,
which is formed by the sum of the individual beampattern
gains corresponding to the common and private data streams.
C. Problem Formulation
The RadCom optimization problem with partial CSIT can
then be defined for a given channel estimate ˆ
Has follows:
min
α, ¯
c,ˆ
P
−X
k∈K
µk(¯
Ck+¯
Rk(ˆ
P))
+λ
M
X
m=1
|αPd(θm)−aH(θm)ˆ
Pˆ
PHa(θm)|2,
(7a)
s.t.X
k0∈K
¯
Ck0≤¯
Rc,k(ˆ
P),∀k∈ K,(7b)
¯
c≥0,(7c)
diag( ˆ
Pˆ
PH) = Pt1
Nt
,(7d)
α > 0,(7e)
(¯
Ck+¯
Rk(ˆ
P)) ≥¯
Rth
k,∀k∈ K,(7f)
where ¯
c= [ ¯
C1,..., ¯
CK]T∈RK×1
+is the variable vector
that contains the portions of the common stream AR, ¯
Rc(ˆ
P),
allocated to the communication users, λis the regularization
parameter to prioritize either communications (maximizing the
AWSR) or radar sensing (minimizing the BSE), and ¯
Rth
kis
the minimum average rate for user-k. Constraint (7b) ensures
that ¯
Rc(P)is decodable by all Kusers. Constraint (7c)
forces the entries of ¯
cto be positive for feasible partitioning
of ¯
Rc(P). Also, constraint (7d) is introduced as an average
power constraint at each transmit antenna to avoid saturation
of transmit power amplifiers in a practical scenario. Finally,
constraint (7f) is the optional QoS rate constraint to guarantee
user rate fairness.
IV. PRECODER OPTIMIZATION WITH PARTIAL CSIT
Based on the work presented in [6], it is proposed that
the non-convex optimization problem in (7) is solved in an
alternating manner by employing the method of Alternating
Direction Method of Multipliers (ADMM).
The new optimization variable v= [α, ¯
cT,vec( ˆ
P)T]T∈
R++ ×RK×1
+×CNt(K+1)×1is introduced to handle all
optimization variables in (7). Then, selection matrices
are defined as Dp= [0(K+1)Nt×(K+1),I(K+1)Nt],
Dc= [0Nt×(K+1),INt,0Nt×K Nt]and Dk=
[0Nt×(K+1+kNt),INt,0Nt×(K−k)Nt]∀k∈ K, and selection
vectors fk= [01×k,1,01×[(K+1)Nt+K−k]]T∀k∈ K, which
are used to extract ¯
Ck=fT
kv.
The user ARs and ¯
Rk(ˆ
P)are expressed as Rc,k(ˆ
P) =
ηc,k(vec( ˆ
P)) = ηc,k(Dpv)and Rk(ˆ
P) = ηk(vec( ˆ
P)) =
ηk(Dpv). Then, (7) is reformulated in an ADMM expression
as follows:
min
v,ufc(v) + gc(v) + fr(u) + gr(u)
s.t.Dp(v−u)=0,
(8)
where u∈R++ ×RK×1
+×CNt(K+1)×1is a new optimization
variable introduced to fit the ADMM optimization definition
and it is initialized as u=v. The functions fc(v)and fr(u)
are defined as fc(v) = −Pk∈K µk(fkv+ηkDpv)and
fr(u) = λPM
m=1 |αPd(θm)−aH(θm)DcuuHDH
c+
Pk∈K DkuuHDH
ka(θm)|2. Also, gc(v)is the
indicator function of the communication feasible set
C=nv
Pk∈K fT
kv≤ηc,k(Dpv)o, and gr(u)
is the indicator function of the radar feasible set
R=nu
diag DcuuHDH
c+Pk∈K DkuuHDH
k=Pt1
Nto.
Finally, (8) is solved in an iterative updating manner as
follows:
vt+1 := arg min
vfc(v) + gc(v)
+ (ρ/2)||Dp(v−ut) + dt||2
2,(9)
ut+1 := arg min
uf(u) + gr(u)
+ (ρ/2)||Dp(vt+1 −u) + dt||2
2,(10)
dt+1 :=dt+Dp(vt+1 −ut+1),(11)
where d∈CNt(K+1)×1is the ADMM scaled dual variable
and ρis the ADMM penalty parameter that controls the
optimization convergence speed. The methods to perform the
v-update and the u-update are explained next.
A. AWSR Maximization Sub-problem
The v-update sub-problem in (9) is reformulated as follows:
min
¯
c,ˆ
P
−X
k∈K
µk[¯
Ck+¯
Rk(ˆ
P)] + ρ
2|| vec( ˆ
P)−Dput+dt||2
2
s.t.X
k0∈K
¯
Ck0≤¯
Rc,k(ˆ
P),∀k∈ K,
¯
c≥0,
diag( ˆ
Pˆ
PH) = Pt1
Nt
,
(¯
Ck+¯
Rk(ˆ
P)) ≥¯
Rth
k,∀k∈ K.
(12)
Due to partial CSIT, the problem in (12) is stochastic in
nature. To solve it, the method proposed in [9] is adapted.
Therefore, (12) is first converted into a deterministic problem
by employing the Sampled Average Approximation (SAA)
method. Then, it is further transformed into a convex problem
by applying the Weighted Minimum Mean Squared Error
(WMMSE) approach and solved by using the Alternating
Optimization (AO) algorithm.
B. BSE Minimization Sub-problem
The u-update sub-problem in (10) is reformulated as fol-
lows:
min
αu,pu
λ
M
X
m=1
|αuPd(θm)−aH(θm)K+1
X
k=1
Dp,kpupH
uDH
p,k
a(θm)|2+ρ
2||Dpvt+1 −pu+dt||2
2
s.t.diag K+1
X
k=1
Dp,kpupH
uDH
p,k=Pt1
Nt
,
αu>0,
(13)
where αu=u1is the first entry of the optimization variable
u,pu= [uK+2, uK+3 , . . . , u(Nt+1)×(K+1)]T∈CNt(k+1)×1,
and Dp,k = [0Nt×(k−1)Nt,INt,0Nt×(K+1−k)Nt]. Although
(13) is originally non-convex, it can be changed into a convex
expression by employing Semi-Definite Relaxation (SDR)
techniques [10].
C. ADMM Algorithm
The ADMM-based optimization algorithm is summarized
in Algorithm 1. The process is repeated iteratively until the
primal residual rt+1 and the dual residual qt+1 of the ADMM
algorithm converge to a value below a predefined threshold ν.
Algorithm 1: ADMM-based RadCom optimization
algorithm with partial CSIT
Input: t←0,vt,ut,dt;
1repeat
2vt+1 ←arg minvfc(v) + gc(v)+(ρ/2)||Dp(v−
ut) + dt||2
2using SAA AR-WMMSE-AO;
3ut+1 ←arg minuf(u) + g(u) +
(ρ/2)||Dp(vt+1 −u) + dt||2
2using SDR;
4dt+1 ←dt+Dp(vt+1 −ut+1);
5rt+1 =Dp(vt+1 −ut+1);
6qt+1 =Dp(ut+1 −ut);
7t←t+ 1;
8until ||rt+1||2≤νand ||qt+1 ||2≤ν
V. PERFORMANCE EVAL UATION
In this section, the joint RSMA-RadCom is evaluated in
terms of its Ergodic Weighted Sum-Rate (EWSR) and Ergodic
Root Beampattern Squared Error (ERBSE) trade-off, where
the average of the optimization results for 200 different
channel realizations are used. It is assumed that the radar
target is located at the 0° azimuth direction, Pt= 20 dBm,
Nt= 4,δ= 0.5,K= 2,µk= 1/K ∀k∈ K,ρ= 1,
ν= 10−2, and the QoS rate constraint ¯
Rth
k= 1 bps/Hz,
∀k∈ K. Also, σ2
k= 1,∀k∈ K is used to generate the
user channel vectors, the CSIT quality scaling factor for all
Kusers is α= 0.6, and λ= [10−9,10−8,...,10−1]Tis
the regularization parameter vector, where increasing lambda
shifts the priority from communications to radar sensing.
In order to highlight the gains brought by empowering the
RadCom with RSMA, the use of Space Division Multiple
Access (SDMA) is considered. SDMA fully treats MUI as
noise, so SDMA operation is enabled by not allocating any
power to the common stream precoder in (1) and omitting ¯
Ck
in (5) [7]. Results for perfect CSIT optimization as described
in [6] are also included in order to demonstrate the robustness
of the RSMA-RadCom as the CSIT quality degrades.
The generated ergodic trade-off curves are plotted in Fig. 2
and the ergodic precoder power allocation is shown in Fig. 3.
With Perfect CSIT, the RSMA-RadCom and SDMA-RadCom
show similar EWSR levels when communications are priori-
tized. This is the effect of directly maximizing the instanta-
neous user rates by mainly employing the user private streams
Fig. 2. EWSR - ERBSE trade-off. Fig. 3. Ergodic Precoder Power Allocation.
as observed in Fig. 3. Nonetheless, the RSMA-RadCom still
presents a slightly better trade-off by employing its common
stream to jointly mitigate the MUI and approximate the desired
radar beampattern in cases where the communication users
are located in azimuth directions near the radar target. As
Radar is given more priority, it is observed that the ERBSEs
of the RadComs become more identical but the EWSR of the
SDMA-RadCom decays at a faster. This can be explained by
noticing from Fig. 3 that the RSMA-RadCom starts allocating
more power to the common stream to generate a directional
beampattern, which also assists in not increasing the MUI for
user-2 in the same level as the SDMA-RadCom. For full radar
priority, both RadComs achieve ERBSE = 0 but the EWSR of
the RSMA-RadCom is 1.75 bps/Hz larger than that of the
SDMA-RadCom.
With partial CSIT, it is observed that the RSMA-RadCom
still outperforms the SDMA-RadCom and when contrasting
the trade-off curves with their Perfect CSIT counterparts, it is
seen that each of them is affected to a different degree. For
instance, the RSMA-RadCom now outperforms the SDMA-
RadCom by 0.47 bps/Hz for communications, and by 1.34
bps/Hz for radar. From Fig. 3, it can be noticed that the
RSMA-RadCom now employs the common stream to a larger
degree to combat MUI imposed by CSIT estimation errors and
by also forcing the MIMO radar beampattern generation. In
turn, the SDMA-RadCom has no other option but to allocate
more power to the precoder of user-1 to maximize the AWSR
and to generate the MIMO radar beampattern. This inevitably
increases the MUI to user-2 and, hence, it achieves a much
lower ergodic rate compared to user-1.
VI. CONCLUSION
An ADMM-based algorithm is introduced which optimizes
the precoders of a joint RadCom to simultaneously maximize
the AWSR and minimize the BSE against a desired highly-
directional transmit beampattern in the presence of partial
CSIT. Analysis of the ergodic performance of the RadCom re-
veals that a RSMA-aided approach enables a more robust and
flexible joint operation to comply with QoS rate constraints
than SDMA. These benefits are due to mainly employing
the common stream to mitigate the MUI introduced by CSIT
inaccuracies and to approximate a directional MIMO radar
beampattern.
REFERENCES
[1] B. Delaney, “Wideband Radar,” in Lincoln Laboratory Journal, vol. 18,
no. 2, pp. 87-88, 2010. [Online]. Available: https://www.ll.mit.edu/sites/
default/files/page/doc/2018-05/LookingBack 18 2.pdf
[2] F. Liu, C. Masouros, A. P. Petropulu, H. Griffiths and L. Hanzo, ”Joint
Radar and Communication Design: Applications, State-of-the-Art, and
the Road Ahead,” in IEEE Transactions on Communications, vol. 68, no.
6, pp. 3834-3862, June 2020.
[3] H. T. Hayvaci and B. Tavli, ”Spectrum sharing in radar and wireless
communication systems: A review,” 2014 International Conference on
Electromagnetics in Advanced Applications (ICEAA), Palm Beach, 2014,
pp. 810-813.
[4] B. Li and A. P. Petropulu, ”Joint Transmit Designs for Coexistence of
MIMO Wireless Communications and Sparse Sensing Radars in Clutter,”
in IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no.
6, pp. 2846-2864, Dec. 2017.
[5] Z. Feng, Z. Fang, Z. Wei, X. Chen, Z. Quan and D. Ji, “Joint radar and
communication: A survey,” in China Communications, vol. 17, no. 1, pp.
1-27, Jan. 2020.
[6] C. Xu, B. Clerckx, S. Chen, Y. Mao and J. Zhang, ”Rate-Splitting
Multiple Access for Multi-Antenna Joint Communication and Radar
Transmissions,” 2020 IEEE International Conference on Communications
Workshops (ICC Workshops), Dublin, Ireland, 2020, pp. 1-6.
[7] Y. Mao, B. Clerckx and V.O.K. Li, “Rate-Splitting Multiple Access for
Downlink Communication Systems: Bridging, Generalizing and Outper-
forming SDMA and NOMA,” EURASIP Journal on Wireless Communi-
cations and Networking, May 2018.
[8] B. Friedlander, “On transmit beamforming for MIMO radar,” in IEEE
Transactions on Aerospace and Electronic Systems, vol. 48, no. 4, pp.
3376–3388, October 2012.
[9] H. Joudeh and B. Clerckx, ”Sum-Rate Maximization for Linearly Pre-
coded Downlink Multiuser MISO Systems With Partial CSIT: A Rate-
Splitting Approach,” in IEEE Transactions on Communications, vol. 64,
no. 11, pp. 4847-4861, Nov. 2016.
[10] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix
inequalities in system and control theory. Siam, 1994, vol. 15.
